1. Martin White – Cambridge ATLAS Martin White ELECTROWEAK INTERACTIONS AND UNIFIED THEORIES XLI Rencontres de Moriond – March 2006

2. 2 Outline Martin White – Cambridge ATLAS Introduction - WMAP and Dark matter - SUSY and WIMP candidates SUSY at the LHC - How does one reconstruct SUSY models at the LHC? - How does one obtain the dark matter relic density from these models? (Will use as an example a recent ATLAS study) - What are the prospects for the LHC in different regions of parameter space? - Will focus on MSSM only, and also largely on mSUGRA benchmark examples - Also, will restrict discussion to relic density measurement Dark matter in UED model – brief discussion of points relevant to LHC At each stage, will try and represent the state of the art

3. 3 Dark matter and WMAP Martin White – Cambridge ATLAS Observations of galaxy rotation curves and the CMB give independent evidence for the existence of dark matter Most recently, WMAP has obtained accurate measurements of the baryonic and matter densities of the universe Fitting to a combination of WMAP and other data gives the best fit values: Assuming the difference gives the dark matter density, we obtain (in units of the critical density): 0.094 <  D h 2 < 0.129 In addition, WMAP favours cold dark matter (non-relativistic when galaxy formation starts) These observations are consistent with WIMP candidates for dark matter Several particle physics models (SUSY, extra dimensions, etc) produce WIMP candidates Thus, LHC potentially has much to say about dark matter problem

4. 4 SUSY and the LSP In SUSY theories, all existing particles have partners with opposite spin statistics In constructing SUSY models, can impose a symmetry called R-parity under which SM particles are even, SUSY particles are odd This has two important phenomenological consequences:  we pair produce sparticles at the LHC  the lightest sparticle (LSP) is absolutely stable Therefore, the LSP is a natural WIMP candidate Which particle is the LSP depends on the point in parameter space. Possible options are gluino, sneutrino, gravitino, lightest neutralino Due to time constraints will focus on neutralino LSP only today It is important to be aware that other WIMP candidates exist both within SUSY,and within other physics models (e.g. extra dimensions, little Higgs with T parity, etc) Martin White – Cambridge ATLAS

5. 5 Measuring SUSY at the LHC: Part I Martin White – Cambridge ATLAS HOW WILL WE OBSERVE SUSY AT THE LHC? STEP 1 Perform inclusive searches. SUSY events have: Large missing energy (due to escaping LSP's) High jet multiplicity (from squark and gluino decay) Isolated leptons (from slepton and gaugino decay) Plot shows the CMS search reach in the jets + E t miss channel in mSUGRA parameter space (5 parameters) Can detect a signal over a large range of parameter space Gives evidence for R-parity conserving SUSY, though need to clarify that it is indeed SUSY

6. 6 Measuring SUSY at the LHC: Part II Martin White – Cambridge ATLAS STEP 2 Try and measure weak scale SUSY parameters through exclusive decay measurements. Can search for kinematic endpoints in the invariant mass distributions of visible decay products of cascade decays Can solve edge equations to reconstruct sparticle masses Can use mass spectrum to try and reconstruct SUSY parameters if we assume a particular breaking framework (e.g. mSUGRA)

7. 7 Measuring SUSY at the LHC: Part III Martin White – Cambridge ATLAS STEP 2 CONTINUED... Most of the work on the measurement of SUSY parameters via endpoints has (unrealistically) assumed that: - the decay chains involved have been determined unambiguously - the particular SUSY breaking scenario is known Furthermore, there are inherent problems in the approach - mass differences are measured much better than absolute masses - decay chains do not exist at all points in parameter space Recent work (Lester, Parker, White) has combined exclusive (endpoint) measurements with inclusive measurements in a Markov Chain Monte Carlo sampling of parameter space - can explore higher dimensional parameter spaces than mSUGRA, thereby reducing model dependence - can include effects of ambiguities and theoretical/experimental uncertainties - obtain greater precision through combination of data

8. 8 Measuring SUSY at the LHC: Part III Martin White – Cambridge ATLAS STEP 2 CONTINUED... Have performed a sample analysis on an mSUGRA point consistent with the WMAP dark matter constraint Uses endpoint data + cross-section of events passing p T miss > 500 GeV Get excellent constraint within mSUGRA parameter space Can clearly see effect of ambiguity in decay chain determination (the two regions correspond to changing the slepton 'chirality' Improves mass measurements (x-section is sensitive to mass scale) The technique can easily be generalised to: - larger parameter spaces - extra observables Lester, Parker, White hep-ph/0508143

9. 9 Obtaining the dark matter relic density: Part I Martin White – Cambridge ATLAS Technically, we have a step 3 in the previous program; need to demonstrate we have SUSY not another model (need spin measurements) Due to time constraints, will assume that we have established this, and can use the LHC mass spectrum measurements as SUSY masses HOW DO WE OBTAIN THE DARK MATTER RELIC DENSITY? In general we find too many neutralinos after the big bang Therefore, need annihilation processes Possible annihilation mechanisms include: (a) slepton exchange (suppressed unless slepton masses are < 200 GeV) (b) annihilation to vector bosons (occurs when LSP acquires a wino or higgsino component) (c) coannihilation with light sleptons (enhanced by mass degeneracies) (d) annihilation to third-generation fermions (can be enhanced by a resonance e.g. where m A is almost exactly twice the LSP mass). Baltz, Battaglia, Peskin & Wizansky hep-ph/0602187

10. 10 Obtaining the dark matter relic density: Part II Martin White – Cambridge ATLAS Within the mSUGRA parameter space, only a few regions are compatible with WMAP constraint The schematic diagram on the right reveals regions in which one of the four annihiliation processes given previously is dominant With no a priori knowledge of which mechanisms are important in nature, need to measure enough at the LHC to narrow down the possible options

11. 11 Obtaining the dark matter relic density: Part III Martin White – Cambridge ATLAS So naively we need to measure some or all of the following: - LSP mass - masses of other light sparticles - mass of heavy higgs m A - components of the neutralino mixing matrix, stau mixing angle So we need measurements of tan  and  There are two obvious strategies: 1. use LHC measurements to try and reconstruct (GUT scale) SUSY model in the manner described previously 2. aggressively target those (weak scale) parameters needed for relic density calculation (1) would be ideal, (2) may be necessary if enough constraints cannot be found to obtain complete set of SUSY model parameters

12. 12 Obtaining the dark matter relic density: Part IV Martin White – Cambridge ATLAS Work by Nojiri, Polesello and Tovey (hep-ph/0512204) is a good example of the second approach They use an existing study of an mSUGRA benchmark model (SPA), but analyse it in the context of a general MSSM Stau (co)annihilation processes are significant at this point, so we'll need to measure the masses of both staus and the stau mixing angle Analysis proceeds in stepwise fashion: STEP (1): USE ENDPOINTS TO RECONSTRUCT SUSY MASSES Have the endpoint measurements shown on the right Pick Monte Carlo experiments to determine mass measurements with associated errors

13. 13 Obtaining the dark matter relic density: Part V Martin White – Cambridge ATLAS STEP (2): USE MASS MEASUREMENTS TO CONSTRAIN ELEMENTS OF NEUTRALINO MIXING MATRIX We obtain only three neutralino measurements in previous step Therefore lack one parameter to constrain matrix – let this be tan  Can therefore reconstruct tan  dependent values for components of the  1 : tan  = 10 tanb Nojiri, Polesello, Tovey hep-ph/0512204 Already conclude that LSP is almost pure bino...

14. 14 Obtaining the dark matter relic density: Part VI Martin White – Cambridge ATLAS STEP (3): CONSTRAIN SLEPTON SECTOR Use measurement of the ratio This is a function of the neutralino mass matrix,   mass,   mass, tan  and   Therefore, can extract a measurement of  , again as a function of tan  Also obtain limits on   mass from lack of observation in cascade decays and from limiting A  to avoid charge breaking minima due to VEV's of charged  scalars Nojiri, Polesello, Tovey hep-ph/0512204

15. 15 Obtaining the dark matter relic density: Part VII Martin White – Cambridge ATLAS STEP (4): CONSTRAIN HIGGS SECTOR Want to now measure tan  Main constraints come from Higgs sector Unfortunately, cannot observe heavy Higgses at SPA point But h is measured – therefore can define confidence bands in m A – tan  plane Can possibly go further: - can set lower limit of 300 GeV and H/A due to non-observation in cascade decays - Could possibly observe H/A via H/A      Can now calculate relic density! Nojiri, Polesello, Tovey hep-ph/0512204 NOTE: The plot shown here is a generic reach plot, and the specific confidence bands are not marked...

16. 16 Obtaining the dark matter relic density: Part VIII Martin White – Cambridge ATLAS STEP (5): CALCULATE RELIC DENSITY The relic density can now be calculated Exact result depends on what we assume we've measured in the Higgs sector Nojiri, Polesello, Tovey hep-ph/0512204 Case 1: only have the minimum constraint in the m A – tan  plane; get upper bound on the relic density Case 2: can set lower limit of 300 GeV on heavy Higgs mass; get much better control on the relic density Case 3: have a direct measurement of the heavy Higgs mass, dominant error comes from tan  In Case 2 get:

17. 17 General prospects for LHC: Part I Martin White – Cambridge ATLAS The example we've just seen was made easier by extensive measurements of sparticle mass spectrum We can't expect this to be true over the whole parameter space WHAT ARE THE GENERAL PROSPECTS AT THE LHC? It is hard to comment on general case, but one can make some generic remarks: 1. always need to measure masses of lightest sparticles and mixing parameters for the lightest neutralino  LHC will succeed in regions with copious production of light sparticles in cascade decays 2. If coannihilations are important, mass differences in cascade decays are small  might not see them (soft taus and leptons are harder to reconstruct) 3. Will need to try and measure tan  and m A – this is not possible in all of parameter space, and tan  is always difficult at the LHC. Recent work has looked at several benchmark points and assessed general capability of LHC and other experiments...

18. 18 General prospects for LHC: Part II Martin White – Cambridge ATLAS Baltz, Battaglia, Peskin and Wizansky (hep-ph/0602187) have analysed 4 mSUGRA benchmark points in the framework of a more general MSSM (parameterized by 24 parameters) Have used the expected measurements from LHC and ILC in a Markov Chain Monte Carlo sampling of the MSSM Also examine interplay between collider and direct/indirect search experiments Benchmark points are chosen at which one of the four annihilation processes given previously is dominant: LCC1: Same as SPS1a. Light sleptons, annihilation to lepton pairs. LCC2: Substantial gaugino-Higgsino mixing, annihilation to vector bosons LCC3: Stau coannihilation important LCC4: A 0 resonance is important At LCC1, get lots of information from kinematic endpoints - get relic density with an accuracy of  7% - could actually improve this using observables correlated to the mass scale which they haven't assumed (see earlier) At other points, things are far less ideal...

19. 19 General prospects for LHC: Part III Martin White – Cambridge ATLAS Consider the point LCC2 Is in focus point region - very large m 0 leads to very heavy squarks and sleptons - won't see these at LHC Don't have enough information to constrain neutralino mixing See ambiguous solutions in  - M 1 plane Linear collider is helpful here (measures polarised chargino and neutralino production cross-sections  constrains mixing matrix Baltz, Battaglia, Peskin & Wizansky hep-ph/0602187

20. 20 General prospects for LHC: Part IV Martin White – Cambridge ATLAS Get similar behaviour at other points, though for different reasons e.g. LCC4 in Higgs funnel region At LHC, can measure only a few parts of SUSY mass spectrum (squarks and first two neutralinos) Can also see h and A, but need to measure  A to constrain relic density Get dramatic improvement a ILC due to ability to measure A width and  (due to observation of third neutralino) The main message is that the LHC and ILC together will be able to make precision measurements, but the LHC alone may struggle unless we are in a favourable region Having observed WIMP at the LHC, would still need to correlate observations with direct search data to see how much of the dark matter density consists of WIMPS, etc Baltz, Battaglia, Peskin & Wizansky hep-ph/0602187

21. 21 UED: Part I Martin White – Cambridge ATLAS Extra dimensions offer an alternative solution to hierarchy problem - instead of cancelling divergences (SUSY), move unification scale to TeV scale In simplest UED model, all SM particles propagate in single extra dimension of size R Each SM particle has infinite tower of Kaluza Klein (KK) excitations - mass of nth KK mode is n 2 /R 2 + m 0 2 (where m 0 is the zero mode mass) - therefore spectrum is highly degenerate at tree level - get significant loop corrections Must conserve KK parity (-1) n where n is the KK level Therefore, first level particles resemble sparticles, get a dark matter candidate in the form of the LKP In minimal UED models, the LKP is the B (1) (KK partner of B 0 )

22. 22 UED: Part II Martin White – Cambridge ATLAS In early universe, B (1) B (1) annihilation is more efficient than SUSY neutralino case Therefore mass range consistent with WMAP is larger, but still within LHC reach of  1.5 TeV Can get coannihilation with e R (1) state if mass degeneracy occurs - note: this actually increases the relic density (B (1) and e R (1) decouple at roughly the same time) Typical mass spectrum shown on left (Cheng et al, hep-ph/0205314) Could observe UED in cascade decays of level 1 particles at LHC (also missing energy, etc) Mass differences might be small  soft leptons and jets (difficult) Also would confuse UED with SUSY unless - level 2 KK particles visible - spin measurements are possible

23. 23 Summary Martin White – Cambridge ATLAS Astrophysical data support existence of WIMP dark matter Many physics models produce good WIMP candidates Prospects for model discovery at the LHC are very good Measuring WIMP properties at LHC is harder, depends on underlying model There are several reasons why we might struggle at the LHC - soft leptons due to mass degeneracies in spectrum - lack of observation of heavy Higgses - lack of constraint on mixing parameters - substantial part of new particle spectrum is too heavy The ILC will considerably extend collider-based knowledge of dark matter Collider experiments will never address the following questions: - how much of the dark matter is comprised of WIMPS - how is the dark matter distributed throughout the universe? - what is the velocity distribution of the dark matter? A combination of collider and direct/indirect search data is required for a complete understanding